Let $f, g : \mathbb{R} \rightarrow \mathbb{R}$ be two real valued functions defined as
where $k_1$ and $k_2$ are real constants. If $(gof)$ is differentiable at $x = 0$, then $(gof)(-4) + (gof)(4)$ is equal to:
\( 4\left(e^{4} + 1\right) \)
\( 2\left(2e^{4} + 1\right) \)
\( 4e^{4} \)
\( 2\left(2e^{4} - 1\right) \)
